On $\pi\mathfrak{F}$-supplemented subgroups of a finite group

Zhang, Li; Chen, Xiaoyu; Guo, Wenbin

doi:10.4171/RSMUP/136-12

π 𝔉

-supplemented subgroups of a finite group

Zhang, Li ¹ ; Chen, Xiaoyu ² ; Guo, Wenbin ¹

¹ University of Scinece and Technology of China, HEFEI, CHINA
² Nanjing Normal University, NANJING, CHINA

Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 175-189.

Résumé

Let $𝔉$ be a class of groups and $G$ a finite group. A chief factor $H / K$ of $G$ is called $𝔉$ -central in $G$ provided $(H / K) ⋊ (G / C_{G} (H / K)) \in 𝔉$ . A normal subgroup $N$ of $G$ is said to be $π 𝔉$ -hypercentral in $G$ if every chief factor of $G$ below $N$ of order divisible by at least one prime in $π$ is $𝔉$ -central in $G$ . The $π 𝔉$ -hypercentre of $G$ is the product of all the normal $π 𝔉$ -hypercentral subgroups of $G$ . In this paper, we study the structure of finite groups by using the notion of $π 𝔉$ -hypercentre. New characterizations of some classes of finite groups are obtained.

DOI : 10.4171/RSMUP/136-12

Classification : 20, 34
Mots-clés : $\mathfrak{F}$-hypercentre, $\pi\mathfrak{F}$-hypercentre, Sylow subgroups, $n$-maximal subgroups

Affiliations des auteurs :

Zhang, Li ¹ ; Chen, Xiaoyu ² ; Guo, Wenbin ¹

¹ University of Scinece and Technology of China, HEFEI, CHINA
² Nanjing Normal University, NANJING, CHINA

@article{RSMUP_2016__136__175_0,
     author = {Zhang, Li and Chen, Xiaoyu and Guo, Wenbin},
     title = {On $\pi\mathfrak{F}$-supplemented subgroups of a finite group},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {175--189},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
     doi = {10.4171/RSMUP/136-12},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-12/}
}

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Zhang, Li; Chen, Xiaoyu; Guo, Wenbin. On $\pi\mathfrak{F}$-supplemented subgroups of a finite group. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 175-189. doi : 10.4171/RSMUP/136-12. http://www.numdam.org/articles/10.4171/RSMUP/136-12/

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